SpaceX SFR: The Small Falcon Rocket

[MatterBeam]

The full post for you to enjoy and discuss, from here: http://toughsf.blogspot.com/2017/10/spacex-sfr-small-falcon-rocket.html

Performance estimates revised: 24 tons expendable, 12-14 tons recoverable to LEO.

The Small Falcon Rocket is a scaled down alternative to SpaceX's Big Falcon Spaceship that fits on top of existing Falcon 9 boosters. 

We will discuss the advantages and disadvantages of such a design.

SpaceX's Big Rockets

 

The BFR, or Big Falcon Rocket, is comprised of the Big Falcon Spaceship and the Big Falcon Rocket booster. It is a scaled down and simplified design based on the ITS, or Interplanetary Transport System.

The BFR is a BIG rocket.

The ITS was revealed in June 2016, although work on the design has begun in 2013 under the name 'Mars Colonial Transporter'. The ITS promised to deliver 300 tons of cargo to Low Earth Orbit, or up to 550 tons if reusability was ignored. It would have massed 10500 tons on the launchpad. The vehicle had a diameter of 12 meters and a height of 122 meters, making it one of the largest rockets ever plausibly considered. 

And the ITS was positively massive.

The upper stage, called the Interplanetary Spaceship, was supposed to hold 1950 tons of propellant with a dry mass of 150 tons. Without a payload, the mass ratio was 14. 

 

The BFR replaced the ITS in September 2017. It is a smaller, more sensible design that SpaceX believes it can actually deliver in the next few years. The diameter is reduced to 9 meters and it will mass 4400 tons on the launchpad. Payload capacity is reduced to 150 tons.

The upper stage BFS should have a dry mass of 75 tons, but Elon Musk states that this might rise to 85 tons due to development bloat and overruns. It holds 1100 tons of propellant, giving it a mass ratio of 13.9.

 

It is important to note that despite being up to 78% smaller than the previous ITS design, the BFS stage maintains the same mass ratio. Why? Because we are now going to scale down the BFS again.

 

Why go smaller?

How big the BFR's booster would be compared to the Falcon 9 booster.

Going big is the best way to reduce the cost per kilogram for sending payloads into orbit. SpaceX jumped from the Falcon 1 to the Falcon 9 because the larger rocket can deliver payloads much more cheaply into space. When first considering options on how to make travel to Mars affordable to the general population, SpaceX immediately came up with a gargantuan tower of rocket fuel over three and a half times larger than the Saturn V! 

 

A big rocket is also easier to develop. It is more forgiving of development bloat that increases mass over time as the designs are perfected. It has larger safety margins and room for many backups, such as multiple engines. 

However, bigger is not always better.
The total development costs will be higher, as large components need large factories. It is much more difficult to test the components too, and a full testing regime of the completed rocket will require launching and even destroying a full-scale model many times. Remember the failed Falcon 9 booster landing attempts, and imagine them replaced with a vehicle eight times bigger.

There is also the fact that the second sure-fire way to reducing launch costs is to have rapid turnover. This involves loading up rockets, sending payloads into space, recovering the rocket and refurbishing it for another launch in a very small time frame, measured in days or even hours. Rapid turnover and minimal refurbishment would allow the space launch industry to more closely resemble existing airline business models. The main benefit of this approach is that a small number of launch vehicles can handle a large volume of missions, critically reducing the initial cost of the vehicles and reducing the amortization rate.

Even if SpaceX manages to develop rockets that liftoff and land several times without needing to go to a workshop, they'd still need to solve the issue that there just aren't enough payloads on the market that need to be lifted into space to fill the BFR, let alone the ITS.

For example, even the BFR's 150 ton payload capacity can cover all of last year's payloads in about two or three launches. Three launches is far from sufficient. Elon Musk is betting that the space industry will be able to fill the BFR's cargo bays with new satellites and LEO payloads once the lowered cost per kg is offered to them... but there will be a long delay between the launch costs being reduced and the industry contracts appearing en masse.

Cost per kg in orbit is only part of the picture.

Waiting for more contracts to appear and bundling them together to use the most of a BFR's cargo capacity is not a good solution. It will force SpaceX to delay launches until the mass delivered to orbit reaches a profitable amount - launching BFRs nearly empty with the usual 2 to 5 ton satellite is surely wasteful and a loss for the company. 

 

The SFR

The SFR, or Small Falcon Rocket, is a possible solution to the development costs, under-utilization and low expected launch rate of the BFR, or Big Falcon Rocket.

The SFR is a scaled down Big Falcon Spaceship sitting on top of an existing Falcon 9 booster. It will carry a smaller payload to orbit, but will have a capacity SpaceX is sure to fill up. Existing Falcon 9 boosters can be mated to a fully reusable upper stage, drastically cutting down on development costs. 

We will now look at the details of the SFR's two stages.

The upper stage is the only new part. It is a BFS scaled down to 3.7 meters diameter, using the same Raptor engines rated at 1900kN of thrust at 375 seconds of Isp. We will call it the SFS, or Small Falcon Spaceship.

The Raptor engine.

The SFS will be (9/3.7)^2: 5.9 times smaller than the BFS. The dry mass is expected to be only 85/5.9: 14.4 tons. It will be 19.7 meters long. 

Based on the mass ratios calculated above, the SFS will be able to hold 187.2 tons of propellant. An SFS with no cargo and full propellant tanks will therefore mass 201.6 tons and have a deltaV of ln(14)*375*9.81: 9708m/s. The Vacuum-optimized Raptor engine is quite large, with a nozzle opening 2.4 meters wide.  It is unlikely that more than one such engine can be fitted under the SFS. It will provide enough thrust for an initial Thrust-to-Weight ratio of 0.96, which must be compared to the current second-stage initial TWRs of 0.8-0.9. For retro-propulsive landing, we will not be able to fit, or even need, the sea-level version of the Raptors. Instead, we will use two of the existing Merlin-1D engines with 420kN of sea-level thrust, but possibly with a lower pressure rating as the thrust generated makes them too powerful for landing. The alternative is the SuperDraco engines with 67kN of thrust and 235s sea-level Isp.

Rocket engines in the Raptor + 2x Merlin configuration would represent 13.2% of the overall dry mass, or 8.1% if the Raptor + 4x SuperDraco configuration is used instead. The Raptor engines are assumed to have a TWR of over 200, so their mass should be lower than 969kg. There are no numbers on the SuperDraco's mass, but it should be at most 50kg. These ratios seem not too outrageous when compared to the 7% engine-mass-to-dry-mass ratio in the BFR's original design.

Merlin-1D engines.

The SFS's mass is based on the 85 ton figure for the BFR's dry mass, but this is a cautious estimate with room given for development bloat and mass budget overruns. The BFR's design on paper gives a dry mass of 75 tons instead. Using the on-paper mass, the SFS could have a dry mass as little as 12.7 tons. 

The SFR's booster is the Falcon 9 Block 4. The booster will mass 22.2 tons when empty, and can hold 410.9 tons of propellant. This gives it a mass ratio of 19.5. The nine Merlin 1D engines have a sea-level Isp of 282s and an vacuum Isp of 311s. Because the booster stage does not spend a long time at sea level and performs most of the burn at high altitudes with negligible air pressure, we will use 300s as a low-ball estimate of the average Isp. The true average might be a few seconds higher. 

Taken all together, the SFR will mass 634.7 tons on the launchpad without any payload in the SFS's cargo bays. It stands 89.7 meters tall. 

We will now calculate how much cargo it can lift into Low Earth Orbit in expendable or reusable mode, and where else it can go.
 

Performance

To achieve a Low Earth Orbit, we will set the deltaV requirement as 9400m/s. In reality, it could be achieved with as little as 9200m/s, but we want decent safety margins.

Expendable mode is the easy part. It assumes every bit of propellant is consumed and the SFR's stages left dry. Using a multi-stage deltaV calculator and setting the Falcon 9 Block 4's Isp to 300s and the SFS's Isp to 375s, we work out that the booster provides 1899m/s of deltaV and the SFS provides 7488m/s for a total of 9388m/s with a payload of 13.7 tons. 

Recoverable mode is harder to calculate. The propellants cannot be completely used up: some must be kept in reserve to perform a retro-propulsive landing burn.

BFR landing.

A landing burn by the SFS requires that about 300m/s of deltaV be held in reserve. This represents 1.65 tons of propellant with Merlin-1Ds or 2 tons of propellant with the SuperDracos. 

The Falcon 9 booster needs to retain 15% of its propellant reserve to make an ocean landing. This gives it a deltaV of 3910m/s, which is largely enough to cancel most of its forwards velocity and make a very soft landing. However, holding back 61.6 tons of propellant means it boosts the SFS by much less. 

In recoverable mode, the SFR's cargo capacity drops to 9 tons.

If the SFS follows the paper designs more closely and achieves a dry mass of 12.7 tons, it will have cargo capacities of 16.7 tons in expendable mode and 12 tons in recoverable mode.

The SFS could achieve a deltaV of 2500m/s after launching on top of a recoverable Falcon 9 booster and without any payload. This is not enough to reach the Moon, so the range of missions the SFR can take payloads on is limited to Low Earth Orbit.

Smaller rockets might solve the problem of having to crane down cargo from the top of a tower.

However, if it is refuelled in orbit, then the entire Solar System is available. It can deliver 50 tons to Low Lunar Orbit (5km/s mission deltaV). It can send 35 tons to the Mars Low Orbit (5.7km/s mission deltaV) or 21 tons to Mars's surface (6.7km/s mission deltaV). Refueling the SFS will take between 16 and 20 tanker launches. 

With 14.4 tons of dry mass and a propellant capacity of 187.2 tons, the SFS has a maximal deltaV of 9.7km/s, enough theoretically to put itself far above Jupiter or even Saturn.

Conclusions

The SFS is a limited vehicle. It is restricted to Low Earth Orbits and can deliver payloads of 9 tons, up to 12 tons, at most. It is far from the multi-purpose machines the BFR or ITS promised to be. 

However, it is enough to dominate the medium lift launch market, as it is fully recoverable. The re-use of existing Falcon 9 boosters and the smaller number of Raptor engines (one per rocket) will drastically slash the development costs compared to something like the BFR. The smaller payloads are easy to fill, meaning every launch is profitable. Multiple launches promises rapid turnover and a maximization of the return on investment on the craft. 

With re-fueling, the SFS in orbit can complete missions that require it to send decent payloads to the Moon and Mars. With minor improvements and operating in fleets of multiple vehicles, it can even match the payload capacity of the BFR to various destinations. 

What do you think?

Edited October 19, 2017 by MatterBeam
Performance estimates revised

[Rakaydos]

Or... you can run the BFS spaceship with 7 SL nozzles as an SSTO, with an "order of magnetude" reduction in payload... from 150 tons to LEO. (so 5-15 tons to LEO)

Same payload range as your suggestion (though lower GTO payload), and tests actual flight hardware for BFR Booster+ship, using the same manufacturing lines they will be using for BFR.  Over all, a true transitional step, not a diversion.

[magnemoe]

Problem is weight of the SFR upper stage, you can not scale thing down so far an keep the dry mass faction. 
Think limit for falcon 9 is around 10 ton to leo reusable but discarding upper stage.
Any weight added to upper stage to make it reusable will cut down directly into reduced cargo capacity, replacing fairing with cargo bay will be worse as you don't haul fairing to orbit so an 1 ton fairing would reduce capacity with 3 ton or something. 

Now with falcon heavy this start making some sense. But you still have the landing engine placement issue

[MatterBeam]

37 minutes ago, Rakaydos said:

Or... you can run the BFS spaceship with 7 SL nozzles as an SSTO, with an "order of magnetude" reduction in payload... from 150 tons to LEO. (so 5-15 tons to LEO)

Same payload range as your suggestion (though lower GTO payload), and tests actual flight hardware for BFR Booster+ship, using the same manufacturing lines they will be using for BFR.  Over all, a true transitional step, not a diversion.

I ran the numbers, the BFR cannot function well as a recoverable SSTO. Its deltaV with no cargo is ln(1185/85)*375*9.81 = 9692m/s. However, it has to launch on lower Isp rocket engines, which will cut this deltaV capacity down below the 9400m/s just to reach orbit... and then it it still needs to reserve some propellant to land with. 

A 400m/s landing deltaV requires 11 tons of propellant using 330s Isp engines. So, we must set the dry mass at 85+11: 96 tons. 

The BFS is no longer an SSTO is we use the 96 ton figure as dry mass. 

The picture changes slightly if we use the strict 75 ton mass with no development bloat. The landing reserve drops to 9.86tons and the mass in orbit can be as low as 84.8 tons. This is enough to make the BFS an SSTO again... but with zero payload capacity. This is also ignoring the 7*969 kg engines it needs to ADD to its existing engines to even liftoff, which will add up to 6.7 tons into its dry mass... 

Just now, magnemoe said:

Problem is weight of the SFR upper stage, you can not scale thing down so far an keep the dry mass faction. 
Think limit for falcon 9 is around 10 ton to leo reusable but discarding upper stage.
Any weight added to upper stage to make it reusable will cut down directly into reduced cargo capacity, replacing fairing with cargo bay will be worse as you don't haul fairing to orbit so an 1 ton fairing would reduce capacity with 3 ton or something. 

Now with falcon heavy this start making some sense. But you still have the landing engine placement issue

The increase in Isp from using Raptor engines instead of the current Merlin engines makes the mass budgets more lenient on an upper stage. However, Raptor engines are too valuable to throw away as expendable upper stage engines, so they are well suited to the fully reusable SFS stage. 

[mikegarrison]

Shrinks never work in aerospace.

[MatterBeam]

2 minutes ago, mikegarrison said:

Shrinks never work in aerospace.

Well, SpaceX shrunk from the ITS to the BFR by a factor 1.8 and maintained the same mass ratio.

[Bill Phil]

1 hour ago, MatterBeam said:

Well, SpaceX shrunk from the ITS to the BFR by a factor 1.8 and maintained the same mass ratio.

For a rocket that has not flown, nor been built. They'd be hard pressed to keep the same mass ratio in practice. Going any farther below will likely reduce the mass ratio.

[mikegarrison]

2 hours ago, MatterBeam said:

Well, SpaceX shrunk from the ITS to the BFR by a factor 1.8 and maintained the same mass ratio.

No they didn't. They threw away one paper rocket and replaced it with another.

[MatterBeam]

42 minutes ago, mikegarrison said:

No they didn't. They threw away one paper rocket and replaced it with another.

The BFR is already in the works and critical components, like ultra-high-mass-ratio propellant tanks and ultra-high-TWR rockets have already been built and tested. I kind of trust that Elon Musk didn't just throw away figures with the usual disregard given for 'paper' projects. 

Scaling down using the same technologies should achieve similar results. 

[DerekL1963]

4 hours ago, MatterBeam said:

Going big is the best way to reduce the cost per kilogram for sending payloads into orbit. SpaceX jumped from the Falcon 1 to the Falcon 9 because the larger rocket can deliver payloads much more cheaply into space

SpaceX jumped from Falcon 1 to Falcon 9 because there was no market for the Falcon 1 - GEO is where the money is.  The Falcon 5 was cancelled for the same reason, insufficient payload to GEO.

[Guest]

This stupid forum won't let me split your OP quote for some dumb reason...

Quote

However, if it is refuelled in orbit, then the entire Solar System is available. It can deliver 50 tons to Low Lunar Orbit (5km/s mission deltaV). It can send 35 tons to the Mars Low Orbit (5.7km/s mission deltaV) or 21 tons to Mars's surface (6.7km/s mission deltaV). Refueling the SFS will take between 16 and 20 tanker launches.

16 to 20 tanker launches is terrible, how about one (basically) BFR launch? Before BFR is built it can still dominate the medium launch market, afterwards we can send large payloads elsewhere. Would have an empty delta-V of 8,955m/s.

I'm beginning to think that Musk's launch cadence is designed solely to handle refueling of these things in orbit.

Quote

What do you think?

It's certainly a viable strategy to reuse upper stages but I don't see it being considered, ever. Musk has his eyes set on Mars, owning the medium launch market wouldn't satisfy him.

[MatterBeam]

38 minutes ago, regex said:

This stupid forum won't let me split your OP quote for some dumb reason...

16 to 20 tanker launches is terrible, how about one (basically) BFR launch? Before BFR is built it can still dominate the medium launch market, afterwards we can send large payloads elsewhere. Would have an empty delta-V of 8,955m/s.

I'm beginning to think that Musk's launch cadence is designed solely to handle refueling of these things in orbit.

It's certainly a viable strategy to reuse upper stages but I don't see it being considered, ever. Musk has his eyes set on Mars, owning the medium launch market wouldn't satisfy him.

The BFR in orbit would need 1100/150: 7.3 launches to be filled up too, so we're only talking two to three times the launch cadence but with a much smaller vehicle. 

The problem as I mentioned with the BFR is that it is unclear whether it is possible to launch the BFRs mostly empty and still make a profit. I find this possibility quite unlikely because if it were the case, then a smaller rocket that is better filled up would make a killing.

The mass ratio and engine Isp of the BFR and SFR are the same, so everywhere the BFR can go, the SFR can do the same. 

Pumping up the launch cadence by refuelling BFRs in orbit still has the problem that there's no money anywhere that will pay for the 8 launches to put a fully fuelled BFR with 150 tons of cargo in orbit. The only envisageable mission would be a large-scale lunar or martian exploration project... but that's mostly up to the governments whether they have the budget. And of course, there's the SLS. 

I agree with your final point though. If Elon Musk pushes for something that doesn't look or sound economically viable, backed up with his personal cash reserve or over-excited investors, then it will get done. We're can't rely on irrational forces though. Consider the SFR as 'sensible' and the BFR as 'visionary'.

[ment18]

The new BFR was specifically sized so that it's development could take place in existing facilities (they are acquiring new ones for more long term manufacture I think).  The cost of refurbishing the BFB might be smaller than the F9 booster because it is much better optimized and fuel cost are less than 1 million for BFR.  You loose the reliability component of the BFS with only one raptor vs 7.  SFS would use two different propellants, a major annoyance based on the locations of current landing prop tanks, landing prop would freeze.  You now have a rocket with 2 or 3 different propellants, wouldn't fit with current launch facilities for F9 anyway.

 

SFS would be really useful from an aerodynamic testing and reentry dynamics.  The payloads for BFR won't appear until BFR flies, so SX just needs to bite the bullet and fix the chicken/egg problem.

[cubinator]

The only advantage I can see for this is testing reentry, and SpaceX plans to do that with BFS anyway. The development would be pretty much a waste of time, because it's really a completely different ship. See how many unanticipated problems they had with "just strap three rockets together". They would be better off just working out the problems involved in BFR directly.

[mikegarrison]

3 hours ago, MatterBeam said:

The BFR is already in the works and critical components, like ultra-high-mass-ratio propellant tanks and ultra-high-TWR rockets have already been built and tested. I kind of trust that Elon Musk didn't just throw away figures with the usual disregard given for 'paper' projects. 

Scaling down using the same technologies should achieve similar results. 

Testing tank construction is TRL 4. That's a heck of a long way from reaching the detail design phase. It's still so early in the TRL process that "paper rocket' might be an over-estimation of how far along they are. Test firing a rocket engine is more like TRL 6, which seems to imply that their engine design is farther along in the process than their ship design. (This is basically to be expected -- airplanes or spaceships are often designed around the available engines.)

Of course it is possible that they are a lot further along in their development process than Musk was willing to show publicly. But it sounds from your post like you are referring to what he showed in his Australian talk. And that was very early PD-level stuff, except for the engine testing.

[Exoscientist]

13 hours ago, MatterBeam said:

The full post for you to enjoy and discuss, from here: http://toughsf.blogspot.com/2017/10/spacex-sfr-small-falcon-rocket.html

 

The Small Falcon Rocket is a scaled down alternative to SpaceX's Big Falcon Spaceship that fits on top of existing Falcon 9 boosters. 

 

 

 I like the idea of making an additional even smaller upper stage for this new system. However, when doing your scaling you should consider that the tanker version of the BFR upper stage likely has a dry mass only in the range 45 to 50 metric tons. This is based on how much smaller the tanker version also was than the spaceship version for the original ITS.

 Then when considering the possible payload in using your new upper stage, the dry mass would be smaller than your estimates, so the payload would be higher.

  Bob Clark

[MatterBeam]

1 hour ago, Exoscientist said:

 

 I like the idea of making an additional even smaller upper stage for this new system. However, when doing your scaling you should consider that the tanker version of the BFR upper stage likely has a dry mass only in the range 45 to 50 metric tons. This is based on how much smaller the tanker version also was than the spaceship version for the original ITS.

 Then when considering the possible payload in using your new upper stage, the dry mass would be smaller than your estimates, so the payload would be higher.

  Bob Clark

Thank you.
I try to be extra-conservative with these estimates for systems that have not been developed yet, but if 75/50: 50% less dry mass can be expected for cargo containers, then we can expect significant increases in payload capacity to orbit.

Looking at the presentation again, it seems that the crewed BFR is expected to be 75 tons, 85 with development bloat, and that the tanker version can be made lighter because the crew spaces can be removed entirely, leaving a spaceship that is mostly propellant tank. 

6 hours ago, mikegarrison said:

Testing tank construction is TRL 4. That's a heck of a long way from reaching the detail design phase. It's still so early in the TRL process that "paper rocket' might be an over-estimation of how far along they are. Test firing a rocket engine is more like TRL 6, which seems to imply that their engine design is farther along in the process than their ship design. (This is basically to be expected -- airplanes or spaceships are often designed around the available engines.)

Of course it is possible that they are a lot further along in their development process than Musk was willing to show publicly. But it sounds from your post like you are referring to what he showed in his Australian talk. And that was very early PD-level stuff, except for the engine testing.

With SpaceX's development and testing pace, TRL4 can be turned into TRL9 in less than five years. 

7 hours ago, cubinator said:

The only advantage I can see for this is testing reentry, and SpaceX plans to do that with BFS anyway. The development would be pretty much a waste of time, because it's really a completely different ship. See how many unanticipated problems they had with "just strap three rockets together". They would be better off just working out the problems involved in BFR directly.

The development of the SFS to fix on top of the Falcon 9 booster is a tiny fraction of the cost of developing the entire BFR, both upper stage and booster, plus building new launch platforms and other infrastructure for a 9m diameter rocket. If SpaceX goes ahead with the BFR, it will very likely end up with a rocket they just can't launch more than once or twice a year without leaving the cargo hold entirely empty. 

That is significant commercial risk.

A lot of Falcon Heavy's problems came from the requirement of cross-feeding the boosters, something that has not been done for rockets not designed from the ground-up to handle cross-feed.

8 hours ago, ment18 said:

The new BFR was specifically sized so that it's development could take place in existing facilities (they are acquiring new ones for more long term manufacture I think).  The cost of refurbishing the BFB might be smaller than the F9 booster because it is much better optimized and fuel cost are less than 1 million for BFR.  You loose the reliability component of the BFS with only one raptor vs 7.  SFS would use two different propellants, a major annoyance based on the locations of current landing prop tanks, landing prop would freeze.  You now have a rocket with 2 or 3 different propellants, wouldn't fit with current launch facilities for F9 anyway.

SFS would be really useful from an aerodynamic testing and reentry dynamics.  The payloads for BFR won't appear until BFR flies, so SX just needs to bite the bullet and fix the chicken/egg problem.

The BFS would have four vacuum-rated Raptors and two (now three) landing Raptors. The SFS will have one vacuum-rated Raptor and two Merlins/four SuperDracos for landing. If the Raptor has anything like the reliability of existing Merlins, then having a single one should not be a problem... second stages on the Flacon 9 have never failed to ignite and re-start. 

The SFS would have to keep a different set of propellants in its header tanks for landing if it uses the SuperDracos. It would be a stop-gap measure until a small ~200kN engine running on liquid methane and liquid oxygen is developed... such as converting a Merlin to lower pressures and a different propellant mix. 

Considering that the Methalox mix is held inside the main tanks for roughly 50 minutes or so, I do not think the insulation requirements will be extreme. Electric heating can be employed. Heat will leak out of the header tanks and into the main tanks if that solution is used... but it will help pressurize the main tanks as they are rapidly drained during launch. 

The decision to make is between the insulation, heated tanks or methalox Merlins, whichever is best. Just slapping on insulation seems like the cheapest solution to develop.

[FleshJeb]

11 hours ago, MatterBeam said:

The BFR is already in the works and critical components, like ultra-high-mass-ratio propellant tanks and ultra-high-TWR rockets have already been built and tested. I kind of trust that Elon Musk didn't just throw away figures with the usual disregard given for 'paper' projects. 

Scaling down using the same technologies should achieve similar results. 

The square-cube law is going to play merry hell with the mass fraction.

[Rune]

15 hours ago, MatterBeam said:

Snip

As @FleshJeb says, the least believable thing in Elon's IAC talk was the fact that the scaled down BFR had the same structural fraction as the larger ITS. Real life doesn't work that way, 'cause square/cube law. But, if you actually believe every word Musk says as gospel, then you have to consider what he said in the AMA a few days later, and you'd have to believe the statement that it is "Worth noting that BFS is capable of reaching orbit by itself with low payload, but having the BF Booster increases payload by more than an order of magnitude ". So basically:

15 hours ago, Rakaydos said:

Or... you can run the BFS spaceship with 7 SL nozzles as an SSTO, with an "order of magnetude" reduction in payload... from 150 tons to LEO. (so 5-15 tons to LEO)

Same payload range as your suggestion (though lower GTO payload), and tests actual flight hardware for BFR Booster+ship, using the same manufacturing lines they will be using for BFR.  Over all, a true transitional step, not a diversion.

...what this guys says.

 

Rune. But hey, interesting number-crunching.

[MatterBeam]

3 minutes ago, Rune said:

As @FleshJeb says, the least believable thing in Elon's IAC talk was the fact that the scaled down BFR had the same structural fraction as the larger ITS. Real life doesn't work that way, 'cause square/cube law. But, if you actually believe every word Musk says as gospel, then you have to consider what he said in the AMA a few days later, and you'd have to believe the statement that it is "Worth noting that BFS is capable of reaching orbit by itself with low payload, but having the BF Booster increases payload by more than an order of magnitude ". So basically:

...what this guys says.

 

Rune. But hey, interesting number-crunching.

For spaceships like these, the vast majority of the volume is just a big propellant tank. You can replace the spaceship with a hollow cylinder of the same volume and still be accurate within 10% of the mass by scaling up and down using area instead of volume. 

Elon Musk's comment seems right... until you do the calculations and realize that it would only be possible to make an SSTO out of the BFS if you also consume the propellant held in reserve for landing. 

Also, I have revised the numbers with my own Excel table calculation instead of relying on an app. Instead of putting 9 tons in orbit, the SFS can put 12 tons. 

[Rune]

18 minutes ago, MatterBeam said:

For spaceships like these, the vast majority of the volume is just a big propellant tank. You can replace the spaceship with a hollow cylinder of the same volume and still be accurate within 10% of the mass by scaling up and down using area instead of volume.

And for just that reason, the square/cube law applies like a ton of bricks. A cylindrical tank's area (A) is directly proportional to R^2, it's volume (V) is directly proportional to R^3. If you multiply V by 0.5 (you halve the tank's fuel capacity), you made R (0.5^1/3)=0,7937 times the initial radius, and A becomes 0.5^(1/2)=0.7071 times the initial area, not half. And the mass of an empty tank scales with area, but the tank's fuel capacity with volume. So yeah, I'd sooner believe the BFS can SSTO, rather than the tanks maintaining their structural fraction when scaled. (Note: I would still be healthily skeptical of both, tough ;))

As to other sources of error, did you take into consideration a SSTO has a rather humongous TWR at the end of the burn, lowering gravity losses? Just an example of why I never trust calculations about launch dV, there are a lot of things that can't be easily modeled with high school algebra.

 

Rune. There are limits to back-of-the-napkin calculations.

Edited October 19, 2017 by Rune

[NSEP]

9 hours ago, cubinator said:

The only advantage I can see for this is testing reentry, and SpaceX plans to do that with BFS anyway. The development would be pretty much a waste of time, because it's really a completely different ship. See how many unanticipated problems they had with "just strap three rockets together". They would be better off just working out the problems involved in BFR directly.

^^ I have to agree on that. Thats my point too.

[mikegarrison]

1 hour ago, MatterBeam said:

With SpaceX's development and testing pace, TRL4 can be turned into TRL9 in less than five years. 

Five Elon Musk promise years is basically the same as 15 years in the actual real world. So we'll see what happens.

[kerbiloid]

15 hours ago, mikegarrison said:

Shrinks never work in aerospace.

But somebody hopes.

Spoiler

P.S.
BFS → DFS (Dyno Falcon Soar).

Edited October 19, 2017 by kerbiloid

[sh1pman]

49 minutes ago, Rune said:

And the mass of an empty tank scales with area

Only is you assume that the tank wall thickness remains constant. If you scale it down proportionally (e.g. multiply by 0.7937), the mass of an empty tank will also scale with volume, keeping mass ratios unchanged.

Edited October 19, 2017 by sh1pman